refactor(background-agent): split manager.ts into focused modules

Extract 30+ single-responsibility modules from manager.ts (1556 LOC):
- task lifecycle: task-starter, task-completer, task-canceller, task-resumer
- task queries: task-queries, task-poller, task-queue-processor
- notifications: notification-builder, notification-tracker, parent-session-notifier
- session handling: session-validator, session-output-validator, session-todo-checker
- spawner: spawner/ directory with focused spawn modules
- utilities: duration-formatter, error-classifier, message-storage-locator
- result handling: result-handler-context, background-task-completer
- shutdown: background-manager-shutdown, process-signal

src/features/background-agent/background-task-notification-template.ts

@@ -0,0 +1,46 @@
+import type { BackgroundTask } from "./types"
+
+export type BackgroundTaskNotificationStatus = "COMPLETED" | "CANCELLED"
+
+export function buildBackgroundTaskNotificationText(input: {
+  task: BackgroundTask
+  duration: string
+  statusText: BackgroundTaskNotificationStatus
+  allComplete: boolean
+  remainingCount: number
+  completedTasks: BackgroundTask[]
+}): string {
+  const { task, duration, statusText, allComplete, remainingCount, completedTasks } = input
+
+  const errorInfo = task.error ? `\n**Error:** ${task.error}` : ""
+
+  if (allComplete) {
+    const completedTasksText = completedTasks
+      .map((t) => `- \`${t.id}\`: ${t.description}`)
+      .join("\n")
+
+    return `<system-reminder>
+[ALL BACKGROUND TASKS COMPLETE]
+
+**Completed:**
+${completedTasksText || `- \`${task.id}\`: ${task.description}`}
+
+Use \`background_output(task_id="<id>")\` to retrieve each result.
+</system-reminder>`
+  }
+
+  const agentInfo = task.category ? `${task.agent} (${task.category})` : task.agent
+
+  return `<system-reminder>
+[BACKGROUND TASK ${statusText}]
+**ID:** \`${task.id}\`
+**Description:** ${task.description}
+**Agent:** ${agentInfo}
+**Duration:** ${duration}${errorInfo}
+
+**${remainingCount} task${remainingCount === 1 ? "" : "s"} still in progress.** You WILL be notified when ALL complete.
+Do NOT poll - continue productive work.
+
+Use \`background_output(task_id="${task.id}")\` to retrieve this result when ready.
+</system-reminder>`
+}